Question: Let $h(x)=\dfrac{1}{x^{11}}$. $h'(x)=$
Answer: The strategy We can first rewrite $h(x)$ as a negative power of $x$. Then, the derivative of $h$ can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ (Remember that this applies even when $n$ is negative.) Rewriting the fraction as a negative power $h(x)=\dfrac{1}{x^{11}}=x^{-11}$ Differentiating using the power rule $\begin{aligned} &\phantom{=}h'(x) \\\\ &=\dfrac{d}{dx}\left(x^{-11}\right) \\\\ &=-11x^{-11-1} \gray{\text{The power rule}} \\\\ &=-11x^{-12} \end{aligned}$ In conclusion, we found that $h'(x)=-11x^{-12}$. This can also be written as $-\dfrac{11}{x^{12}}$ (all equivalent forms are accepted).